How many 10 digits numbers can be written by using the digits 1 and 2a...
To find the number of 10-digit numbers that can be written using the digits 1 and 2, we need to consider the following:
1. Choosing the positions for the digits:
- Since there are 10 digits in the number, we need to choose the positions for the digits 1 and 2.
- Each position can be filled with either 1 or 2, so there are 2 choices for each position.
- Therefore, the total number of ways to choose the positions for the digits is 2^10 = 1024.
2. Choosing the digits:
- Once we have chosen the positions for the digits, we need to assign the digits 1 and 2 to those positions.
- The number of ways to choose 1 position for the digit 1 from the 10 chosen positions is 10C1 = 10.
- The number of ways to choose 2 positions for the digit 2 from the remaining 9 chosen positions is 9C2 = 36.
- Therefore, the total number of ways to choose the digits is 10C1 * 9C2 = 10 * 36 = 360.
3. Arranging the digits:
- Once we have chosen the positions and digits, we can arrange them in those positions in a single way.
- Therefore, the number of ways to arrange the digits is 1.
4. Final answer:
- The final answer is obtained by multiplying the number of ways to choose the positions, the number of ways to choose the digits, and the number of ways to arrange the digits.
- Final answer = 1024 * 360 * 1 = 368,640.
Therefore, the correct answer is option 'B' (210 is incorrect).
How many 10 digits numbers can be written by using the digits 1 and 2a...
2X2X2X2X2X2X2X2X2X2=1024